The range of recently discovered phenomena in complex oxide heterostructures, made possible owing to advances in fabrication techniques, promise new functionalities and device concepts. One issue that has received attention is the bistable electrical modulation of conductivity in ferroelectric tunnel junctions (FTJs) in response to a ferroelectric polarization of the tunnelling barrier, a phenomenon known as the tunnelling electroresistance (TER) effect. Ferroelectric tunnel junctions with ferromagnetic electrodes allow ferroelectric control of the tunnelling spin polarization through the magnetoelectric coupling at the ferromagnet/ferroelectric interface. Here we demonstrate a significant enhancement of TER due to a ferroelectrically induced phase transition at a magnetic complex oxide interface. Ferroelectric tunnel junctions consisting of BaTiO3 tunnelling barriers and La(0.7)Sr(0.3)MnO3 electrodes exhibit a TER enhanced by up to ~10,000% by a nanometre-thick La(0.5)Ca(0.5)MnO3 interlayer inserted at one of the interfaces. The observed phenomenon originates from the metal-to-insulator phase transition in La(0.5)Ca(0.5)MnO3, driven by the modulation of carrier density through ferroelectric polarization switching. Electrical, ferroelectric and magnetoresistive measurements combined with first-principles calculations provide evidence for a magnetoelectric origin of the enhanced TER, and indicate the presence of defect-mediated conduction in the FTJs. The effect is robust and may serve as a viable route for electronic and spintronic applications.